A029047 Expansion of 1/((1-x)*(1-x^3)*(1-x^6)*(1-x^10)).
1, 1, 1, 2, 2, 2, 4, 4, 4, 6, 7, 7, 10, 11, 11, 14, 16, 16, 20, 22, 23, 27, 30, 31, 36, 39, 41, 46, 50, 52, 59, 63, 66, 73, 78, 81, 90, 95, 99, 108, 115, 119, 130, 137, 142, 153, 162, 167, 180, 189, 196, 209, 220, 227, 242, 253, 262, 277, 290, 299, 317, 330
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,1,-1,0,-1,2,-1,0,-1,1,0,-1,1,0,1,-1).
Crossrefs
Cf. A008620.
Programs
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Maple
M:= Matrix(20, (i,j)-> if (i=j-1) or (j=1 and member(i, [1, 3, 6, 14, 17, 19])) then 1 elif j=1 and member(i, [4, 7, 9, 11, 13, 16, 20]) then -1 elif j=1 and i=10 then 2 else 0 fi): a:= n-> (M^(n))[1,1]: seq(a(n), n=0..80); # Alois P. Heinz, Jul 25 2008
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Mathematica
CoefficientList[Series[1/((1-x)(1-x^3)(1-x^6)(1-x^10)),{x,0,70}],x] (* Harvey P. Dale, Feb 06 2020 *) -
PARI
Vec(1/((1-x)*(1-x^3)*(1-x^6)*(1-x^10))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
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PARI
a(n)=floor((2*n^3+60*n^2+527*n+1243+9*(n+1)*(-1)^n+(120*(n\3+1)*[1,1,-2]+20*[61,41,0])[n%3+1])/2160) \\ Tani Akinari, May 07 2014
Formula
a(n) = floor((2*n^3 + 60*n^2 + 567*n + 9*n*(-1)^n + 2160)/2160 - (n/18)*[(n mod 3)=2] + (1/5)*([(n mod 6)=0] - [(n mod 6)=5])). - Hoang Xuan Thanh, Jul 06 2025
Comments